From the sound of it you have a simple aerial distribution system. The thing (amplifier) that feeds the four TVs is either a box attached to your aerial, or it could be a box in the loft. Either way they both do a similar job: A signal from the aerial comes in to the box, it is amplified and split four ways, each output then feeds a TV in your house.
As others have said, the WPS100 is a power supply for the amplifier. What's confusing for most people is that the power from it goes in to the aerial cable which at first sight appears to be a very odd thing to happen. That's why these things get mistaken for an amplifier in their own right. What's happening is that the amplifier (on the roof/in the loft) uses phantom power. The same bit of aerial cable that carries TV signals down from the roof/loft also carries power but in the opposite direction. Here's a graphic I did a long time ago for a similar kind of question. It shows the signal flow (the pale blue/green arrows) and the power flow (red arrows).
If you have your head around the signal flow then you should start to realise why you're having trouble getting the Sky signal from the I/O box in to your aerial system so it can be seen on other TVs. The answer is that the signal flow direction is going in the opposite direction to what you need.
In order to get the Sky I/O box signal in to your aerial distribution amp two things would need to happen. Presuming you still want to watch Freeview on the TVs when they're not being used to watch Sky, then the first is that you need an I/O box that has an RF Input as well as an RF output. You might already have one of these but I don't think you've mentioned it yet. Second, the signal direct from the aerial (wherever it lives) needs to be rerouted to come directly to the Sky I/O box RF input, then the the signal from the I/O box output then gets run up to the aerial amplifier. In effect then, you need a long loop of cable coming down and then up the side of your house. In other words, what's involved is a substantial rewire job for a DIYer to undertake.
Beyond the basics of the rewire there's some other considerations: Putting the signal through so much cable will knock the quality down a bit. Whether the signal from your local transmitter is strong enough once it gets to your aerial to then withstand these losses is difficult to predict without some accurate signal level measurements. This means then that unless you're employing the services of an aerial installer with the right kind of gear who can do a comprehensive and accurate site survey before you go ahead (
and you should expect to pay for that service) then the wiring job will be something of a leap of faith. The second issue is more minor and easier to check: It's whether all the other TVs have analogue tuners. The I/O box signal from the Sky box uses the older analogue signal format. Lots of TV remotes have the TV/DTV button to switch between the analogue and digital tuners (or some other way of achieving the same effect), but not every new TV still does. TV manufacturers are looking for ways to cut costs and ditching the analogue tuner as a less-often-used feature is starting to become more common, so it's worth checking before you start spending any more cash.
This is normally the point when the beleaguered OP asks if there's another way to achieve the same thing. (Yes, surprise surprise, those of us who have been here a while have seen numerous folk go round and round on the same old merry-go-round.) The common 'go-to' ideas are video senders or HDMI distribution using CAT6 baluns. I'll cut to the chase; it will be cheaper and more effective to get your aerial distribution system changed professionally than exploring the video sender idea for 3+ TVs. HDMI over CAT cable will give better results but it will cost quite a bit more to implement.
